Bayesian Flow Networks

TL;DR

Bayesian Flow Networks (BFNs) are a new generative modeling approach that updates independent distributions via Bayesian inference, enabling efficient, differentiable, and flexible generation for both discrete and continuous data, with competitive results.

Contribution

This paper introduces BFNs, a novel generative model that simplifies diffusion processes by removing the forward step and supports gradient-based guidance in discrete domains.

Findings

Achieved competitive log-likelihoods on image datasets

Outperformed discrete diffusion models on language modeling

Supports gradient-based sample guidance in discrete data

Abstract

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input to a neural network that outputs a second, interdependent distribution. Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models; however it is conceptually simpler in that no forward process is required. Discrete and continuous-time loss functions are derived for continuous, discretised and discrete data, along with sample generation procedures. Notably, the network inputs for discrete data lie on the probability simplex, and are therefore natively differentiable, paving the way for gradient-based sample guidance and few-step generation in discrete domains such as language modelling. The loss function directly optimises data compression and places no restrictions on the network architecture. In our experiments BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.